Last updated: 8/15/2021 ## Grade 2 - Operations and Algebraic Thinking

 Subject: Mathematics (NYS P-12 Common Core)
 Unit Title: Grade 2 - Operations and Algebraic Thinking
 Approx. Number of Weeks: 1st Semester

#### Unit Summary:

Develop quick recall of basic addition facts/related subtraction facts, up to and including 20 (30 in 3 minutes).

Extend their knowledge of number properties and operations using number patterns. (e.g. skip counting [5s,10s, multiples of 100s,10s,1s] can build foundations for understanding multiples and factors).

Solve problems using their understanding of addition and subtraction relationships (combining or separating sets, use of # lines, etc.)

Add and subtract multi-digit numbers and solve problems (using place value and the commutative and associative properties)

Develop fluency with efficient procedures for adding and subtracting whole numbers and use them to solve problems.

Solve problems to develop initial understanding of multiplication (as repeated addition and with arrays). Collaboration & Communication Creativity & Innovation Critical Thinking & Problem Solving Research & Information Fluency Social & Emotional Intelligence

### 1. What will students know and be able to do?

#### Standards:

 2.OA.1 - Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 2.OA.2 - Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. 2.OA.3 - Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.4 - Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

#### Essential Understandings:

Students will understand that…

Place value understanding can be used to develop strategies to represent and solve problems.

#### Essential Questions:

How can I best show my thinking to solve the problem?

#### Students will know:

A conceptual understanding of addition can be used to develop procedures and solve problems.

Addition and subtraction have properties; rules to solve problems.

Work with equal groups of objects can lay foundations for multiplication.

#### Students will be able to:

Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

FLUENCY STANDARD !

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (2.OA.1)

FLUENCY STANDARD !

Fluently add and subtract within 20 using mental strategies. (2.OA.2)

**By end of Grade 2, know from memory all sums of two one-digit numbers.

Work with equal groups of objects to gain foundations for multiplication.

Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. (2.OA.3)

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. (2.OA.4)

Color Code Key: GapsMajor Clusters, Additional Clusters, Supporting Clusters

### 3. What learning activities will students participate in?

#### Learning Activities:

Number Talks /Mental Math and Computation Strategies K-5-- from Math Solutions K-5

Mathematics Handbook Series/Math to Learn, Math to Know- Teacher Handbook from Great Source

Mathematics Handbook Series/Math to Learn, Math to Know- Teacher’s Resource Book- Reproducibles from Great Source

#### Discipline Specific Considerations:

Vocabulary – Specialized and High Frequency

Addition, subtraction, operation, sum, difference, equal, total, skip count, odd, even, addend, array, equation, number pattern, related facts (fact family), multiplication, array, compare, symbol, rows, columns, doubles, combine, separate, number line, repeated addition, solve, number sentence, commutative property, associative property, unknown, one-stop problem, two-step problem

*Students do not develop a rich and deep sense of number and place value if instructional focus is on the process of computation without representation and modeling of concepts.

A larger number cannot be subtracted from a smaller number, IN FACT, this can be done and results in a negative number and the understanding of integers and the continuous nature of number.

*Zero is not a part of the counting sequence. Zero represents the empty set and is not an even or odd number.

The answer is always at the right side of the equals sign, IN FACT, both sides of the equal sign should always represent the same value.

Common Core State Standards:  Standards for Mathematical Practice

Standard 1:    Make sense of problems and persevere in solving them

Standard 2:    Reason abstractly and quantitatively

Standard 3:    Construct viable arguments and critique the reasoning of others

Standard 4:    Model with Mathematics

Standard 5:    Use appropriate tools strategically

Standard 6:   Attend to precision

Standard 7:  Look for and make use of structure

Standard 8:  Look for and express regularity in repeated reasoning 